CONTROL THEORY III Mock Exam 2 Mock Exam 2

Find the transfer function of a system with state-space parameters given by equations (3a), (3b), (3c), and (3d). $A = \begin{bmatrix} 0 & -1 \\ 1 & 2 \end{bmatrix}$ (3a) $B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$ (3b) $C = \begin{bmatrix} 1 & 1 \end{bmatrix}$ (3c) $D = \begin{bmatrix} 0 \end{bmatrix}$ (3d) Where: A is the state matrix, B is the input matrix, C is the output matrix, and D is the direct transmission matrix. [25marks]

a) With the aid of block diagram explain the principle of operation of a computer control system [15marks]

b) Enumerate 5 areas of application and 5 advantages of digital control system. [10marks]

The state matrix of a system is given by equation (Q4), comment on the stability of this system and determine the eigenvector of A. $A = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$ (Q4)